1. Field Of The Invention
The present invention relates to methods and apparatus for producing a repeatable motion profile from biased piezoelectric transducers and particularly to such methods and apparatus that are operated in an open loop configuration with a nonzero DC voltage bias.
2. Description Of The Prior Art
Open loop operation of piezoelectric transducers (PZT) is known to be advantageous for reasons of simplicity and cost. However, since piezoelectric transducers are not linear gain devices, the physical motion profile of the PZT is not directly proportional to the voltage profile. In addition, PZTs exhibit hysteresis so that the effect of a voltage change depends on previous voltage history, and they also exhibit creep, a continuous slowly decaying motion after movement in response to a sudden change in voltage. All of these effects are due to the fact that piezoelectric ceramics are produced in a polarized state, which is necessary for the piezoelectric effect in the first place. At a particular bulk polarization, the PZT responds to a voltage change by changing its length proportional to the PZT gain; however, the bulk polarization changes in response to the applied voltage change with a characteristic time proportional to the temperature and field strength. This in turn changes the gain and, hence, the length which produces a feedforward effect which is responsible for the nonlinear way the PZT responds and which is undesirable when repeatable motion is desired from a PZT. These undesirable effects have, at times, been overcome in the prior art by the addition of a distance measuring sensor that has a linear response to displacement and whose signal is fed back to the PZT voltage driver to correct for PZT nonlinearities. However, the additional required physical and electronic apparatus utilized in such a prior art approach, can significantly increase the cost of the PZT system, and, moreover, system bandwidth may be reduced because of propagation delays in the feedback loop and system noise may be increased by the contribution from the displacement sensor.
Another prior art attempt at overcoming these undesirable effects has involved repetitively driving the PZT with the same voltage waveform with a time averaged net voltage of zero volts. Using this prior art approach, open loop PZT motion can be extremely repeatable because the polarization change over any cycle averages to zero and compensating for the PZT nonlinearities by modifying the voltage waveform is a very effective way of producing small, repeatable motions to within fractions of a percent, however there are still problems with this approach, particularly where a non zero net DC voltage is required for the application. An example of this prior art approach is disclosed in U.S. Pat. No. 5,051,696 to Elings which discloses a nonlinear voltage compensation method. Unfortunately there are many important applications in which a non zero net DC voltage is necessary or at least extremely convenient and, thus, this prior art approach provides an undesirable solution. For example, this prior art approach would be unsatisfactory when it was necessary to provide DC voltages to alter the physical location of the scanning region in an atomic force scanning microscope (AFM) or a scanning tunnel microscope (STM) for AFM or STM applications, in which a probe was scanned across the surface of a sample to determine properties of the surface, such as typography or magnetic field strength, so that these properties can be displayed for viewing. Other examples in which a non zero net DC voltage is desired are in unipolar voltage applications or applications that need to use as much of the PZT range as possible--since the typical usable PZT voltage range is very nonsymmetric about zero. However, since operating a PZT with a net DC bias produces a follow-up polarization that changes the net gain over time, this would destroy the motion repeatability in the long term, thus proving unsatisfactory. This property, called drift, is analogous to creep and can be as high as a few percent per time decade. Accordingly, although U.S. Pat. No. 5,051,646 teaches a method for attempting to provide repeatable motion in a PZT, it does not teach or suggest a method for compensating for the resultant drift in biased PZTs. In fact, U.S. Pat. No. 5,051,646 totally ignores the very real problem of drift. Consequently, it would be desirable to find a simple, cost effective way to compensate for drift so as to try to ensure the long term repeatability of the PZT motion over time.
C. V. Newcomb and I. Flinn, in an article entitled "Improving The Linearity of Piezoelectric Ceramic Actuators," Elec. Lett. 18 (1982), pages 442-444, disclosed the fact that, for small strains the PZT extension is linear with respect to applied charge and they proposed a prior art "charge drive," in which the PZT was driven by accounting for the change applied to the drive. In practice, however, it has been found that the small leakage currents which normally exist in any electronics system makes it almost impossible to keep this prior art system at any nonzero DC bias over long periods. Over time the bias simply leaks away. Thus, the prior art charge drive circuit proposed by Newcomb and Flinn would need to periodically switch between "charge" and "voltage" modes of operation to maintain the bias, such as occurs in U.S. Pat. No. 4,263,527 to Comstock, by way of example, thereby adding a significant complexity to the operation. This added complexity is one reason that such prior art charge drive circuits are rarely used.
These disadvantages of the prior art are overcome by the present invention.